The control force of the parafoil represents a crucial indicator in the selection of servo motors for precision airdrop systems. This paper proposes an Arbitrary Lagrange Euler (ALE)-based method for calculating the control force of the parafoil. The method is demonstrated through calculations of the control force within different control strokes. The calculated results are consistent with the experimental result, with the error being less than 5%. On this basis, the coupling mechanism and dynamic change law of the control force under the airdrop condition are investigated. It is found that the control force reaches the maximum when the control rope is pulled down to the target control stroke, and then gradually decreases until it reaches a steady state. The influence of control parameters on control force is examined. The findings indicate that when the control speed is fixed, an increase in control stroke results in a rise in both maximum control force and steady-state control force, but a decline in the control force rising rate. When the control stroke is held constant, an increase in control speed results in an increase in maximum control force, while the steady-state control force remains almost unchanged. In comparison to the control stroke, the control speed has less influence on the maximum control force. The findings of this study can provide a theoretical foundation for the design of the parafoil control rope and the selection of servo motor.

Further missions of China's planetary exploration projects to the Venus, the Jupiter and others have been initiated, and the key technical research is underway. However, these planets have significantly different atmospheric environments from those of the Earth and the Mars, with dense atmospheres and higher atmospheric pressures. Previous successful planetary explorations reveal that the aerodynamic deceleration process in such complex planetary atmospheric environments requires multi-stage parachutes and transonic/supersonic conditions for parachute opening and operation. Meanwhile, the nominal diameter of the first stage guide parachute is significantly smaller than that of the main parachute and the forebody diameter. With few related research reports, the fluid structure interaction mechanism and the aerodynamic characteristics between two-stage parachutes of different sizes and the forebody are still unclear. In this research, based on conical ribbon parachutes and disk-band-gap parachutes suitable for dense atmospheric planetary exploration missions, the fluid structure interaction mechanism of flexible parachutes in different planetary atmospheric environments is numerically studied using the immersion boundary method, and the aerodynamic characteristics with different freestream Mach numbers, canopy types, atmospheric components, and parameter to diameter ratios are investigated. Results show that in the atmospheric environment of the Titan, the conical ribbon canopy (with a diameter ratio of 0.3) steadily descends at transonic speeds, and the projected area of the canopy increases over time. The drag coefficient reaches its maximum at Mach number 1.5, while its fluctuation monotonically increases with the increase of the Mach number. In addition, at Mach number 0.95, the canopies exhibit extremely severe oscillation when the diameter ratios are 0 and 1. In contrast, in the atmospheric environment of the Jupiter, when the freestream Mach number is transonic, the change in the projected area of the conical ribbon canopy becomes smaller over time. The drag coefficient and its fluctuation will monotonically increase with the increase of the Mach number, and the lateral force coefficient and its fluctuation reach their maximum at Mach number 1.5. Finally, a comparison is made between the stable descent process of parachutes in the atmospheric environments of the Titan, the Venus, and the Jupiter, showing that the conical ribbon canopy in the Jupiter atmospheric environment has the best performance, a larger drag coefficient, and better stability.

At present, the key technical researches are carried out for the future exploration missions to dense atmosphere planets such as Jupiter. As a necessary aerodynamic decelerator for planetary exploration missions with dense atmosphere, parachutes face several big challenges, such as complex transonic/supersonic unsteady aerodynamic characteristics. Thus, it is necessary to study deeply and make clear the transonic/supersonic unsteady flow mechanisms around the parachute systems and its aerodynamic characteristics; however, these are still unknown to date. In this study, parachute structure systems are designed based on the Galileo exploration mission. Using the parachute models, the numerical simulations were conducted to investigate the complex flow phenomena and unsteady aerodynamics of parachute systems with different diameter ratios of capsule to canopy, under different freestream Mach numbers. As a result, it is found that when a parachute 2-body model with a bigger diameter ratio of capsule to canopy is placed in transonic flows, the wake of the forebody (capsule) is strong, and the shock wave in front of the canopy is weak. When the canopy shock moves upstream, the pressure fluctuation inside the canopy surface exhibits 3 stages of changes: high-frequency large-amplitude, low-frequency small-amplitude, and high-frequency small-amplitude. It is also found that in the supersonic flow cases, the amplitude and frequency of pressure fluctuations inside the canopy increase significantly, especially at Mach 2.0. This is due to the strong interactions between the shedding vortex of the wake and the shock wave in front of the canopy. However, for the parachute model with a small diameter ratio, the important shock waves in front of the canopy is not observed, and high-frequency and small-amplitude pressure variations remain, which is affected directly by the frequency and intensity of wake vortex shedding. In summary, as the Mach number increases, the amplitude and frequency of pressure fluctuations increase, and the average pressure distribution also increases, and the law of its influence becomes more complex.

The material damage of parachute may occur in parachutes at high speeds, and the growth of tearing may finally lead to failure of aerospace mission. In order to study the damage mechanism of parachute, a material failure model is proposed to simulate the failure of canopy fabric. The inflation process of supersonic parachute is studied numerically based on Arbitrary Lagrange Euler (ALE) method. The ALE method with material failure can predict the transient parachute shape with damage propagation as well as the flow characteristics in the parachute inflation process, and the simulated dynamic opening load is consistent with the flight test. The damage propagation mechanism of parachute is then investigated, and the effect of parachute velocity on the damage process is discussed. The results show that the canopy tears apart by the fast flow from the initial damaged area and the damaged canopy shape leads to the asymmetric change of the flow structure. With the increase of Mach number, the canopy tearing speed increases, and the tearing directions become uncertain at high Mach numbers. The dynamic load when damage occurs increases with the Mach number, and is proportional to the dynamic pressure above the critical Mach number.